When doing statistical characterization, excellent nominal characterization accuracy is essential. Nominal correlation for path delays of within 2% of Spice reduces the uncertainty that must be accounted for through statistical distributions.
Keeping the runtime under control with acceptable throughput is very important, especially for random variations. That's because they have to be modeled on a per-transistor (intra-cell) basis. In addition, a given transistor may be significantly affected by random variations of a number of parameters in terms of the measurable electrical impact seen on the cell as a whole.
The brute-force approach to characterization is to take measurements for every transistor over the entire range of variation of every parameter. But what's really of interest is reducing the number of needed circuit measurements, which requires considerable intelligence and sophistication. The techniques applied should efficiently determine how to prune out measurements that do not add to the overall cell's statistical distributions of electrical properties, preserving accuracy while reducing runtime.
An acceptable result of such measurement optimization is that statistical characterization takes less than 10 times the time required for a single PVT-point (process, voltage, and temperature) characterization.
Systematic variations are characterized by capturing the sensitivity of overall cell electrical behavior to these variations. Because these variations are not random, their use allows for a reduction in the range of statistical variation that must be modeled, or, in other words, a reduction in uncertainty. These variations also require fewer measurements for characterization. As a result, they provide far better runtime than statistical characterization.
With chip designers utilizing multi-vendor solutions, it becomes imperative for characterization to support all major statistical model formats, such as s-ECSM and CCS-VA, and formats for statistical timing-analysis tools, such as Magma's Quartz SSTA and Extreme Design Automation's GoldTime. Finally, SSTA characterization must be automated to ensure ease of use comparable to traditional characterization.
Khalid Islam is the senior product manager with the Custom Design Business Unit at Magma Design Automation, San Jose, Calif.
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